A Symbolic-Numeric Method for Solving Boundary Value Problems of Kirchhoff Rods

V. G. Ganzha, E. W. Mayr und E. V. Vorozhtsov (Editoren)

Stichwörter: computer algebra, hair modelling, Kirchhoff models

Bibtex

@INPROCEEDINGS{shu-2005-symbolic,
      author = {Shu, Liu and Weber, Andreas},
      editor = {Ganzha, V. G. and Mayr, E. W. and Vorozhtsov, E. V.},
       pages = {387--398},
       title = {A Symbolic-Numeric Method for Solving Boundary Value Problems of Kirchhoff Rods},
   booktitle = {Computer Algebra in Scientific Computing (CASC '05)},
      series = {Lecture Notes in Computer Science},
      volume = {3718},
        year = {2005},
       month = sep,
   publisher = {Springer-Verlag},
    keywords = {computer algebra, hair modelling, Kirchhoff models},
    abstract = {We study solution methods for boundary value problems associated
                    with the static Kirchhoff rod equations. Using the well known
                    Kirchhoff kinetic analogy between the equations describing the
                    spinning top in a gravity field and spatial rods, the static
                    Kirchhoff rod equations can be fully integrated. We first give an
                    explicit form of a general solution of the static Kirchhoff
                    equations in parametric form that is easy to use. Then by
                    combining the explicit solution with a minimization scheme, we
                    develop a unified method to match the parameters and integration
                    constants needed by the explicit solutions and given boundary
                    conditions. The method presented in the paper can be adapted to a
                    variety of boundary conditions. We detail our method on two
                    commonly used boundary conditions.},
        isbn = {3-540-28966-6},
  conference = {Computer Algebra in Scientific Computing (CASC '05)}
}